Download hep-ph - Royal Holloway, University of London

arXiv:hep-ph/0410114v2 14 Dec 2004
OUTP-04/17P
Asymmetric Sneutrino Dark Matter
and the Ωb/ΩDM Puzzle
Dan Hooper1, John March-Russell2, and Stephen M. West2
1
Astrophysics Dept., University of Oxford,
Denys Wilkinson Building, Oxford OX1 3RH, UK
2
Rudolf Peierls Centre for Theoretical Physics,
University of Oxford, 1 Keble Road, Oxford OX1 3NP, UK
(October, 2004)
Abstract
The inferred values of the cosmological baryon and dark matter densities are strikingly
similar, but in most theories of the early universe there is no true explanation of this
fact; in particular, the baryon asymmetry and thus density depends upon unknown, and
a priori unknown and possibly small, CP-violating phases which are independent of all
parameters determining the dark matter density. We consider models of dark matter
possessing a particle-antiparticle asymmetry where this asymmetry determines both the
baryon asymmetry and strongly effects the dark matter density, thus naturally linking Ωb
and Ωdm . We show that sneutrinos can play the role of such dark matter in a previously
studied variant of the MSSM in which the light neutrino masses result from higherdimensional supersymmetry-breaking terms.
1
Introduction
For some time it has been apparent that the inferred values of the cosmological baryon
and dark matter densities are strikingly similar. For example, the latest WMAPdetermined range for the dark matter density, 0.129 > ΩCDM h2 > 0.095, is within a
factor of a few of the combined WMAP and big-bang nucleosynthesis determined value
of the baryon density, 0.025 > Ωb h2 > 0.012 [1, 2]. In the vast majority of models of
the early universe, the cosmological baryon and dark matter densities are independently
determined. The surviving baryon density is set by a baryon asymmetry generated during baryogenesis, and thus depends upon unknown, and a priori unknown and possibly
small CP-violating phases, as well as unknown baryon-number violating dynamics. In
contrast, the dark matter density is set by the ‘freeze-out’ of the interactions that keep
the dark matter in equilibrium, and is independent of the dynamics of baryogenesis. In
particular, although weakly-interacting massive particles at the TeV-scale naturally have
a relic density of O(1) times the critical density, this is not at all the case for baryons.
The Boltzmann equations show the size of the baryon relic density in the absence of an
asymmetry is O(10−11 ). Thus the comparative closeness of the baryon and dark matter densities poses a puzzle. One possible approach to this problem is to more closely
integrate the dynamics of baryogenesis with that of the origin of dark matter. In particular, it is natural to consider models where the dark matter and baryon sectors share a
quantum number, either continuous or discrete, which provides a relation between their
surviving number densities and thus energy densities.1
Specifically, in this letter we consider models of dark matter possessing a particleantiparticle asymmetry where this asymmetry strongly effects the dark matter density,
and through the electroweak (EW) anomaly, determines the baryon asymmetry, thus
naturally linking Ωb and ΩCDM . (A noteworthy early attempt along these lines which
shares some features with our model is contained in Ref. [9].) The shared quantum
number clearly requires that the dark matter particle not be it’s own antiparticle, so the
putative dark matter candidate cannot be the standard LSP neutralino of the broken
Minimal Supersymmetric Standard Model (MSSM). In fact, we will show in sections 3
and 4 that sneutrinos can play the role of such dark matter in a previously studied
variant of the MSSM in which the light neutrino masses result from higher-dimensional
supersymmetry-breaking terms [10, 11, 12, 13, 14]. This model preserves all the successes
of the MSSM, such as stability of the weak scale and unification of gauge couplings, while
being, at least in part, testable at the LHC.
Before we proceed to the calculation of the relic dark matter and baryon densities
and the details of our model, it is useful to consider some aspects of the idea of a shared
quantum number determining the ratio of baryon to dark matter. First, consider the
simplified case in which, to a very good approximation, the dark matter and baryon
sectors cannot exchange their conserved quantum number after its first production. As
an example, consider the situation in which the asymptotic baryon number B = 1 states
of the Standard Model (SM) have global charge, q, while the lightest asymptotic states
1
An alternate approach is to invoke a form of the Anthropic Principle, see, for example, Ref. [3].
Other ideas are explored in Refs. [4, 5, 6, 7, 8].
1
(with mass mdm ) in a hidden sector carry charge, Q. Then conservation of global charge
implies that q (nb − nb ) = −Q (ndm − ndm ), where the n’s are the number densities
of the indicated (anti)particles. Further assume that interactions in both sectors are
strong enough such that almost all antiparticles are eliminated by annihilation with
their particles (assuming Q/q < 0 for simplicity). This implies
nb = cndm with c = |Q/q|,
(1)
which in turn leads to
Ωb
mb nb
mb
=
=c
.
(2)
Ωdm
mdm ndm
mdm
Thus the energy densities are indeed related, but the ratio is only naturally O(1) if the
ratio of the baryon to dark matter masses is not too small. It is important to note that
this disfavours models of the above type where the dark matter candidate is a ‘hidden
sector’ particle and favours a particular class of models where the dark matter candidate
has weak scale mass, its mass arising either from electroweak symmetry breaking, or from
the dynamics which drives electroweak breaking, such as supersymmetry softly broken
at the weak-scale.2
As a consequence, the naive statement of Eq.(1) also requires modification as the
approximation of negligible interactions between the two sectors, and thus negligible exchange of the shared conserved quantum number, does not hold in realistic models. In
this situation, the ratio of the conserved quantum number stored in the two sectors, c,
is not simply given by Q/q, but is determined by the ‘chemical’ equilibrium conditions
between the two sectors just before the freeze-out of the relevant interactions. We will
further discuss this point in section 2. Moreover, two other alterations to the naive relation Eq.(2) can be present. First, the shared quantum number may only be conserved
modulo n, in which case ‘self’ annihilations may occur, and second, it is not always the
case that dark matter interactions are efficient enough such that ndm ≪ ndm . Nevertheless, as we argue in the next section, a careful consideration of such models shows that
a version of the naive statement Eq.(2) can indeed hold.
2
The Effect of a Matter-Antimatter Asymmetry on
the Density of a Thermal Relic
If there were an asymmetry between the density of dark matter particles and dark antimatter particles in the early universe, it may have a considerable effect on the relic
density calculation [15]. In this section, we review the relic density calculation for a
single species, two species with no asymmetry and two species with an asymmetry.
If dark matter consists of a single species, the relic density calculation is straightforward. The most common example of a single species dark matter candidate would be
2
In extensions of the SM such as the MSSM where many gauge-non-neutral fermionic and scalar
states also gain mass at this scale, the beta-function coefficient for SU (3)QCD sharply increases as
energies are reduced below the weak scale, and the confinement scale and thus baryon mass is naturally
not very much smaller than mweak .
2
a neutralino LSP with negligible coannihilations with other SUSY particles. In such a
case, the resulting relic density is simply
1.04 × 109 xF
1
Ωh2 ∼
,
=
√
MPl
g∗ (a + 3b/xF )
(3)
where MPl is the Planck mass, xF is the WIMP’s mass over the freeze-out temperature,
g∗ is number of relativistic degrees of freedom available at freeze-out and a and b are
related to the WIMP’s self-annihilation cross section by σv = a + bv 2 + O(v 4 ), v being
the relative velocity of the annihilating WIMPs. For a weakly interacting relic, xF is
generally about 20 and varies only mildly with changes in the cross section or mass.
If we instead consider a dark matter candidate and its antiparticle, the calculation
becomes somewhat different. Labeling these species 1 and 2, we now have each particle’s
self-annihilation cross section, σ11 = σ22 , and the particle-antiparticle annihilation cross
section, σ12 = σ21 . In the limit that σ12 is much smaller than σ11 , we simply get two
decoupled species which each provide the relic density of Eq.(3). Otherwise, the effective
cross section becomes σ11 + σ12 for each species. For the two species together, a density
of
1
1.04 × 109 xF
(4)
Ωh2 ∼
=2×
√
MPl
g∗ (a11 + a12 + 3(b11 + b12 )/xF )
is produced. This case is essentially the calculation of the density of a relic with the
coannihilation of a degenerate particle [16].
If an asymmetry exists between the number density of particles and antiparticles in
the early universe, again this calculation becomes modified. The most well known example of this is the baryon-antibaryon asymmetry which leads to the current baryon density
of the universe despite the very large baryon-antibaryon annihilation cross section. In
such a case, where the particle-particle and antiparticle-antiparticle annihilation cross
sections (σ11 and σ22 ) are zero, or negligibly small, the minimum relic density can be
related to the magnitude of the particle-antiparticle asymmetry:
Ωh2min = Ωh2bary
A
m
,
Abary mbary
(5)
where Ωh2bary is the current density of baryons in the universe, A and Abary are the
particle-antiparticle asymmetries of our relic and of baryons, defined by A = (n − n)/n.
Abary is known to be of the order of 10−9 . m and mbary are the masses of our relic and
of baryons (i.e. the proton mass). Of course, if the particle-particle annihilation cross
section for the relic is not negligible, Eq.(5) will not hold. There will be a generic tendency
for the density of a relic to move towards this value as a result of an asymmetry, however.
To accurately assess the effect of an asymmetry on the thermal relic abundance, the
effective cross sections must be determined by integrating over the thermal history. In
particular, for each species separately, the densities predicted are
1.04 × 109 xF
1
Ω1 h2 ∼
=
√
g∗ (a11,eff + a12,eff + 3(b11,eff + b12,eff )/xF )
MPl
3
(6)
and
1.04 × 109 xF
1
,
Ω2 h2 ∼
=
√
MPl
g∗ (a22,eff + a21,eff + 3(b22,eff + b21,eff )/xF )
(7)
where the effective cross sections are given by
a11,eff = a11 ,
a22,eff = a22 ,
b11,eff = b11 ,
b22,eff = b22 ,
a12,eff = xF
a21,eff = xF
R∞
xF
a12
x2
R∞
b12,eff = 2x2F
b21,eff = 2x2F
a12
xF x2
R∞
xF
R∞
xF
b12
x3
b12
x3
e−x
e−x +A
e−x +A
e−x
dx,
e−x
e−x +A
e−x +A
e−x
dx,
(8)
dx,
dx.
The factor, e−x /(e−x + A), is the depletion of the second species due to the asymmetry
at a temperature, T = m/x. The effect of this depletion depends on the size of the
asymmetry and the cross sections involved. If the estimate of Eq.(5) is considerably less
than the standard two-species result of Eq.(4), then the asymmetry has little impact
and the sum of Eqs.(6) and (7) is nearly equal to Eq.(4). If, however, the estimate of
Eq.(5) is larger than the standard two-species result, the relic density moves from the
value found with Eq.(4) towards that of Eq.(5). If σ11 /σ12 is small, then the result will
be closer to Eq.(5). If σ11 /σ12 is large, then the density will be less modified. Note that
in some cases, the effect of an asymmetry can be to lower the density of a relic by up to
a factor of two. This occurs when σ11 and σ12 are comparable thus efficiently deplete the
second species while leaving the first largely uneffected.
Although these effects are rather model dependent, the net effect can be large regions
of parameter space which predict the observed density of dark matter for a WIMP with
a mass near m ∼ mp ΩWMAP h2 /Ωbary h2 , for a matter-antimatter asymmetry similar to
that for baryons. For concreteness, we consider a specific example of such a model in the
following section.
3
An Example: Mixed Sneutrino Dark Matter
Within the context of the Minimal Supersymmetric Standard Model (MSSM), sneutrinos
do not make a very appealing dark matter candidate. They annihilate quite efficiently,
resulting in a relic density smaller than the observed dark matter density for sneutrinos
lighter than about 500 GeV. Furthermore, their elastic scattering cross section is sufficiently large to be easily observed by direct dark matter experiments. Thus it is natural
that in contrast to other supersymmetric dark matter candidates, sneutrino dark matter
has received considerably less attention [17].
Looking beyond the vanilla MSSM, however, it is quite easy to construct a viable
model for sneutrino dark matter. For example, sneutrinos could mix through A-terms
with a singlet forming a mixed sneutrino state. This would reduce the annihilation cross
section, potentially providing the appropriate quantity of dark matter, as well as reduce
the elastic scattering cross section to experimentally acceptable levels. In fact, such a
4
scenario has previously been discussed as a way to reconcile the results of the direct dark
matter detection experiments DAMA and CDMS [12]. These models have light sneutrino
mass eigenstates which are mixtures of left-handed ‘active’ sneutrinos, and right-handed
‘sterile’ sneutrinos.
Such mixing naturally arises in models in which the light neutrino masses are generated by supersymmetry breaking effects [10, 11, 13, 14]. The importance to us of these
models is that the light sneutrino states share a non-anomalous (B − L)-symmetry with
the baryons which is only weakly broken by the Majorana neutrino masses. In analogy to
the Giudice-Masiero mechanism for the Higgs µ-term there exists a global symmetry that
forbids a direct mass, MR NN, and neutrino Yukawa coupling, λLNHu , involving the SM
singlet right-handed neutrino superfield N, but allows non-renormalizable couplings to
a supersymmetry-breaking hidden-sector field T . The right-handed neutrino mass and
the neutrino Yukawa coupling, λLNHu , then only arise from 1/Mplanck -suppressed terms
involving the fundamental supersymmetry breaking scale mI ∼ (vMpl )1/2 , where v is the
weak scale. The relevant terms in the Lagrangian are
L=
Z
T†
T †T
T †T T †
d4 θ h NN + h̃ 2 N † N + hB
NN + . . . +
M
M
M3
!
Z
T
d θ g LNHu , (9)
M
2
where all dimensionless couplings g, h, etc, are taken to be O(1). The structure of the
Lagrangian can be enforced by some simple symmetries [10, 11, 13], including R-parity,
which leads to a stable lightest supersymmetric particle (LSP) dark matter candidate.
After supersymmetry is broken in the hidden sector at the scale mI , the F and A components of the field T acquire intermediate scale vevs, hFT i ∼ hAT i2 ∼ m2I . Substituting
these vevs into the Lagrangian shows that after SUSY breaking, there arises: (1) a neutrino Yukawa coupling of size ∼ 10−7 − 10−8 , (2) right-handed neutrino and sneutrino
masses at the weak scale, (3) a weak-scale trilinear scalar A-term, and (4) a right-handed
sneutrino lepton-number violating B-term with magnitude B 2 ∼ (few × 100 MeV)2 .
These together lead to two sources of neutrino masses, a tree level see-saw contribution,
as well as a dominant 1-loop contribution, leading to a consistent and attractive neutrino
phenomenology [10, 13].
More relevant for us, the sneutrino mass matrix squared is
ν̃ ∗ n
m2L
√1 Av sin β
2
√1 Av sin β
2
m2R
!
ν̃
n∗
!
,
(10)
where we have ignored the small lepton number violating B-term for the moment. Therefore mixing between the left-handed ‘active’ sneutrino, ν̃, and the right-handed ‘sterile’ sneutrino, ñ, occurs,
producing the light mass eigenstate ν̃1 = −ν̃ sin θ + ñ∗ cos θ,
√
where tan 2θ = − 2Av sin β/(m2R − m2L ), with m2R = MN2 + m2R,soft and m2L =
m2Z cos 2β/2 + m2L,soft . Since the coupling of the lighter sneutrino eigenstate to the Z
is suppressed by sin θ, the direct LEP experimental constraints are weakened, and the
calculation of the sneutrino relic abundances is modified. A numerical analysis of the
susy parameter space shows that a mixing sin θ ≃ 0.3 is quite natural.3 (The B 2 massterm splits the CP-even and CP-odd components of ν̃1 by the amount δ ∼ cos2 θB 2 /m1 .
3
Note that the size of the A terms is limited by considerations of vacuum stability [14].
5
This can have important consequences for detection, potentially making consistent the
DAMA and CDMS experiments depending upon parameters [12]. For the purposes of
our discussion this splitting is irrelevant.)
We now turn to the calculation of the relative asymmetry in the sneutrino and
baryon sectors. The method is a simple adaption of the standard ‘chemical’ equilibriation
techniques applied to, for example, the calculation of the ratio B/(B − L) in the SM [19]
or MSSM [20] in the presence of anomaly-induced baryon number violating processes in
the early universe. For each species of particle we introduce a chemical potential, µA ,
and for each interaction in equilibrium, say A + B ↔ C + D there is a corresponding
relation among chemical potentials µA + µB = µC + µD . Note that when in thermal
(not necessarily chemical) equilibrium the CP-conjugate species A has µA = −µA . The
asymmetry in particle-antiparticle number density for the relevant case of µ ≪ T and a
species of mass m is given by n − n = gT 2 µ/6 for T ≫ m, and is Boltzmann suppressed
< m.
by exp(−m/T ) for T ∼
The electroweak B +L anomaly interactions provide an efficient mechanism to transmute between B- and L-number densities, at least above the EW phase transition temperature Tc where they are rapid. Our task is to calculate the ratio of sneutrino to baryon
asymmetries at Tc where the exchange between the two sectors switches off. (We implicitly assume that the EWPT is 1st order so that anomaly-induced interactions drop out
of equilibrium below Tc . For realistic values of Tc the results of our calculation are not
particularly sensitive to this assumption.) Above the EWPT temperature the chemical
potentials for all SM gauge bosons vanish, so, for example, members of an EW doublet
have the same µ. Moreover, efficient flavour mixing among quarks induced by EW interactions such as uLi + φ01 ↔ uRj , involving the neutral up-like higgs, or dLi + φ02 ↔ dRj ,
involving the neutral down-like higgs, ensures that only one chemical potential, say that
for uL , is required to describe the quark sector. Similarly, efficient flavour mixing among
> 10−7, so that only one chemical potenthe light neutrinos holds for mixing angles, θij ∼
tial, µνL , is needed to describe the neutrino and sectors. In addition non-perturbative
EW processes can be thought of creating, say, a neutron made of lhd quarks, and a lhd
neutrino out of the vacuum for each generation. When this process is in equilibrium it
imposes an additional relation which can be written
3µuL + µνL = 0.
(11)
When the MSSM susy spectrum is included the analysis becomes more involved. To
simplify the analysis let us first assume at a temperature T (with T > Tc ) that the
MSSM susy spectrum, including k rhd sneutrinos can be considered light (m <
∼ T ). As
shown in Ref.[20] the usual soft-susy-breaking terms and supersymmetric partners of the
SM interactions lead to enough relations among the chemical potentials that only 3 are
needed for an independent set: µ0 ≡ (µφ10 − µφ20 )/2 in the neutral Higgs sector, µuL , and
µνL . In our case we must add an additional k light (m < Tc ) rhd neutrinos and sneutrinos
with their associated potentials µνRi and µν̃Ri , but we also have A-term interactions
between the lhd and rhd sneutrinos, and the very small lepton-number violating rhd
sneutrino B-term. These together enforce the conditions
µν˜R = µν˜L = µνL ,
6
(12)
where the first equality arises from A-term mediated interactions (as the A terms are
O(mw ) it is simple to show that these are in equilibrium), and the second equality arises
from SU(2)w × U(1)Y gaugino interactions.4 In terms of µ0 , µuL , and µνL , the condition
Eq.(11) is unchanged in the case of the MSSM + k rhd neutrino supermultiplets.
The final step in the calculation of the relative number densities proceeds by expressing the relevant densities in terms of the independent chemical potentials. For the
baryon number density B the result is simply
B = 6T 2 µuL .
(13)
For the sneutrino asymmetry the result depends upon the mass spectrum of the sneutrino
mass eigenstates relative to Tc . In the range of parameters of interest to us where the
light sneutrino eigenstate ν̃1 is the LSP we have m1 < Tc . On the other hand the heavier
eigenstate ν̃2 can have m2 > Tc or m2 < Tc . If both eigenstates satisfy m < Tc then the
sneutrino density is (allowing for a possible k such states)
S=
kT 2
2kT 2
(µν̃L + µν̃R ) =
µνL
3
3
(14)
while if only m1 < Tc then S is half as large. Finally using the non-perturbative relation
Eq.(11) we find that
A
S
k
k
=− =
to
(15)
Abary
B
3
6
depending on m2 . We view k = 1 as most likely, so we specialize to that case in the next
section. Finally we mention that a full susy-mass-threshold dependent calculation of the
relative asymmetries introduces only small corrections to this result (see Ref.[20] for a
similar analysis in the MSSM case).
In the end the vital point is that independent of whatever dynamics at scales E > Tc
produces an asymmetry in either the baryon sector, or in the neutrino or sneutrino
sector, the (B + L)-anomaly-induced interactions together with EW gaugino and A-term
interactions automatically distributes the asymmetry between the baryons and the light
sneutrino states, with a predictable A/Abary ratio. The asymmetry could originate from,
e.g. a GUT-based baryogenesis mechanism, or maybe more interestingly in the context of
the sneutrino dark matter model there is the possibility that it could arise via a resonant
leptogenesis mechanism at the TeV-scale as discussed in Ref.[14]. The end result is that
> A/Abary > 1/6 independent of the source of the asymmetry.
we expect 1/3 ∼
∼
4
Asymmetric sneutrino and baryon abundances
We will now apply the formalism of section 2 to the sneutrino model. Given the value of
> A/Abary > 1/6, we expect the role of the matter-antimatter asymmetry to be most
1/3 ∼
∼
4
Note that the rhd neutrinos only interact via the small neutrino Yukawa, λ ∼ 10−7 − 10−8 , so
these states are not in equilibrium at T ∼ Tc . However, µνR does not enter our final expression for the
sneutrino to baryon number density ratio, so its value is irrelevant.
7
important for sneutrinos with masses on the order of m ∼ few × mp ΩWMAP h2 /Ωbary h2 ≃
30 GeV. For this reason, we will focus on the mass range of about 10 to 80 GeV. In this
range, the most important annihilation channel is s-channel Z-exchange to fermions.
This is a p-wave amplitude, and has no a-term in the expansion in v 2 (see section 2).
This is also only a sneutrino-antisneutrino process (i.e. σ11,22 , not σ12,21 ). Other channels
include t-channel neutralino and chargino exchanges to neutrinos and charged leptons.
The channel to charged leptons includes both a and b terms in the v 2 expansion. Additionally, sneutrino-sneutrino pairs (or antisneutrino-antisneutrino pairs) can annihilate
via t-channel neutralino exchange to neutrino pairs of the same flavor. This is the only
contribution to σ12,21 in this model.
The annihilation cross sections for the neutralino and chargino exchange processes
depend on the masses and mixings of these exchanged particles, although the Z-exchange
channels do not. We have adopted the parameters M1 =300 GeV, M2 =300 GeV, µ=600
GeV and tan β = 50 throughout our calculation. Additionally, there is the mixing angle
between the sneutrino and the singlet which can be varied. This quantity has the effect
of reducing all electroweak couplings of the sneutrino eigenstate by a factor of sin2 θ, i.e.
reducing the annihilation cross sections by a factor of sin4 θ.
Finally, one can consider the s-channel exchange of Higgs bosons to bb (or ZZ and
W W − above the appropriate mass thresholds). This process is not suppressed by sin4 θ.
The efficiency of this process depends on the magnitude of the trilinear scalar coupling
and is only important near the Higgs resonance (mν̃ ≃ mh /2) or above the gauge boson
mass thresholds.
+
Our results are shown in figure 1. The shaded regions of the parameter space predict
a relic density within the range measured by WMAP (0.129 > ΩCDM h2 > 0.095). In
the left frame, no matter-antimatter asymmetry was included. This frame can be easily
understood as requiring greater suppression of electroweak couplings (smaller sin θ) as the
sneutrino mass approaches the Z mass. The dip at 56-59 GeV is due to s-channel higgs
exchange to bb. In the right frame, a matter-antimatter asymmetry of A/Abary ≃ 1/6 was
included. To further illustrate this effect, we show the result of this calculation across
one value of sin θ in figure 2. Below about 30 GeV, the matter-antimatter asymmetry
has little effect on the calculation and the solid and dot-dashed lines fall nearly on top
of each other. In the range of roughly 30-70 GeV, however, the asymmetry pulls the relic
density above the standard symmetric result into the range favored by WMAP. Above
this range, sneutrino-antisneutrino annihilation decreases, leading to larger relic densities
for the case with no asymmetry. The relic density for the asymmetric case, however, is
largely determined by the sneutrino-sneutrino annihilation cross section in this region,
so does not increase as rapidly, therefore resulting in a relic density much closer to the
preferred value, even for mν̃ > 70 GeV.
5
Indirect Detection
Sneutrinos in the mass range we have studied here annihilate dominantly through schannel Z exchange in the early universe. This annihilation channel consists of a b-term
8
Figure 1: The regions of parameter space which provide the quantity of mixed sneutrino
cold dark matter measured by WMAP, 0.129 > ΩCDM h2 > 0.095. In the left frame, the
standard calculation with no matter-antimatter asymmetry is used. In the center frame
the effect of a matter-antimatter asymmetry with A/Abary ≃ 1/6 is included, while in
the right frame a matter-antimatter asymmetry A/Abary ≃ 1/3 is assumed. Notice the
much larger regions of acceptable parameter space in cases with asymmetry. We use the
following parameters: M1 =300 GeV, M2 =300 GeV, µ=600 GeV, tan β = 50 and mh =115
GeV. The region above the solid line is excluded by measurements of the invisible Z decay
width [18].
in the expansion σv = a+ bv 2 + O(v 4 ), and thus is very inefficient for annihilations at low
velocities which take place in the late universe. At low velocities, the process ν̃ ν̃ → νν,
via t-channel neutralino exchange, is the most important annihilation channel.
Given these characteristics, searches for gamma-rays, anti-protons, positrons or other
particles produced in sneutrino annihilations in the Galactic halo are quite inefficient.
Due to the rather large elastic scattering cross sections of sneutrinos, however, indirect
detection techniques involving the capture of dark matter in bodies such as the Sun can
be very effective.
Neutrino telescopes detect neutrinos produced in dark matter annihilations in the
core of the Sun by observing ’tracks’ of muons generated in charged current interactions.
If our sneutirno 5 dark matter candidate is of muon or tau flavor, the flux of muons generated in this way in a detector at Earth is of the order of 10−12 cm−2 s−1 [12], in conflict
with data from the Super-Kamiokande and MACRO experiments, for example [21]. If
the candidate, however, is of electron flavor, these bounds can be easily averted.
6
Conclusions
In the standard freeze-out calculation for a weakly interacting dark matter relic, there
is little reason to expect a density of dark matter which is similar to the density of
baryons, short of anthropic arguments. In this letter, however, we have presented an
5
In the model presented, the dark matter candidate is actually an antisneutrino and consequently
antineutrinos will be produced by dark matter annihilations in the sun.
9
Figure 2: The thermal relic density as a function of mass for sneutrinos+antisneutrinos
with no asymmetry (dot-dash), with a matter-antimatter asymmetry of A/Abary ≃ 1/6
(solid) and the estimate of Eq.(5) (dots). The relic density range favored by WMAP is
bound by dashed lines (0.129 > ΩCDM h2 > 0.095). sin θ=0.3, M1 =300 GeV, M2 =300
GeV, µ=600 GeV, tan β = 50 and mh =115 GeV have been used. See text for details.
explanation for the similarity between these two quantities. Our solution introduces
an asymmetry between dark matter particles and anti-particles which is related to the
baryon-antibaryon asymmetry. This leads to a natural dark matter relic density of the
same order of magnitude as the baryon density.
As an example, we considered a mixed sneutrino dark matter candidate which transfers its particle-antiparticle asymmetry to the baryons through the electroweak anomaly.
We carry out the relic density calculation for such a candidate and find substantial regions of parameter space in which the observations of WMAP can be satisfied. With
no asymmetry, only a narrow strip of parameter space can provide the observed relic
density.
Acknowledgments
We wish to thank Yuval Grossman for a useful correspondence. SW is supported by
PPARC Studentship Award PPA/S/S/2002/03530.
References
[1] D. N. Spergel et al., Astrophys. J. Suppl. 148 (2003) 175 [arXiv:astro-ph/0302209].
[2] S. Eidelman et al. [Particle Data Group Collaboration], Phys. Lett. B 592, 1 (2004).
[3] F. Wilczek, arXiv:hep-ph/0408167.
[4] A. Kusenko and M. E. Shaposhnikov, Phys. Lett. B 418, 46 (1998)
[arXiv:hep-ph/9709492].
10
[5] K. Enqvist and J.
[arXiv:hep-ph/9803380].
McDonald,
Nucl.
Phys.
B
538,
321
(1999)
[6] D. H. Oaknin and A. Zhitnitsky, arXiv:hep-ph/0309086.
[7] D. H. Oaknin and A. R. Zhitnitsky, arXiv:hep-ph/0406146.
[8] G. R. Farrar and G. Zaharijas, arXiv:hep-ph/0406281.
[9] D. B. Kaplan, Phys. Rev. Lett. 68, 741 (1992).
[10] N. Arkani-Hamed, et al, Phys. Rev. D 64, 115011 (2001) [arXiv:hep-ph/0006312];
N. Arkani-Hamed, et al, arXiv:hep-ph/0007001;
[11] F. Borzumati and Y. Nomura, Phys. Rev. D 64, 053005
[arXiv:hep-ph/0007018]; F. Borzumati, et al, arXiv:hep-ph/0012118;
(2001)
[12] D. R. Smith and N. Weiner, Phys. Rev. D 64, 043502 (2001) [arXiv:hep-ph/0101138];
D. Tucker-Smith and N. Weiner, arXiv:hep-ph/0402065.
[13] J. March-Russell and S. M. West, arXiv:hep-ph/0403067.
[14] T. Hambye, J. March-Russell and S. M. West, JHEP 0407 (2004) 070
[arXiv:hep-ph/0403183]; S. M. West, arXiv:hep-ph/0408318.
[15] K. Griest and D. Seckel, Nucl. Phys. B 283, 681 (1987) [Erratum-ibid. B 296, 1034
(1988)].
[16] K. Griest and D. Seckel, Phys. Rev. D 43, 3191 (1991).
[17] T. Falk, K. A. Olive and M. Srednicki, Phys. Lett. B 339, 248 (1994)
[arXiv:hep-ph/9409270]; L. E. Ibanez, Phys. Lett. B 137, 160 (1984); J. S. Hagelin,
G. L. Kane and S. Raby, Nucl. Phys. B 241, 638 (1984); L. J. Hall, T. Moroi and
H. Murayama, Phys. Lett. B 424, 305 (1998) [arXiv:hep-ph/9712515]; T. Han and
R. Hempfling, Phys. Lett. B 415, 161 (1997) [arXiv:hep-ph/9708264].
[18] T. Hebbeker, Phys. Lett. B 470, 259 (1999) [arXiv:hep-ph/9910326].
[19] J. A. Harvey and M. S. Turner, Phys. Rev. D 42, 3344 (1990).
[20] T. Inui, T. Ichihara, Y. Mimura and N. Sakai, Phys. Lett. B 325, 392 (1994)
[arXiv:hep-ph/9310268].
[21] G. Giacomelli [MACRO Collaboration], Braz. J. Phys. 33, 211 (2003)
[arXiv:hep-ex/0210006]; I. De Mitri [MACRO collaboration], arXiv:hep-ex/0212055.
11